Dissipation, Emergent Quantization and Quantum Fluctuations

Abstract

We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems and thermal field theories is discussed and the doubled variables are related to quantum noise effects. The 't Hooft proposal, according to which the loss of information due to dissipation in a classical deterministic system manifests itself in the quantum features of the system, is analyzed and the quantum spectrum of the harmonic oscillator is shown to be originated from the dissipative character of the original classical deterministic system.

Invited talk at the International Workshop DICE2002 "Decoherence, Information, Complexity and Entropy" - Piombino (Tuscany), September 2-6, 2002

References in corpus (1)

• Quantization, group contraction and zero point energy

Cited by in corpus (6)

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• Quantum features in statistical observations of "timeless" classical systems
• A holographic map of action onto entropy
• Emergence of classical gravity and the objective reduction of the quantum state in deterministic models of quantum mechanics
• Emergence from irreversibility
• Emergent phenomenology from deterministic Cartan-Randers systems